cold fish vs unpleasant person

cold fish and unpleasant person both are nouns.

Word	Noun	Adjective	Verb	Adverb
cold fish	Yes	No	No	No
unpleasant person	Yes	No	No	No

As nouns, unpleasant person is a hypernym of cold fish; that is, unpleasant person is a word with a broader meaning than cold fish:

Other hypernyms of cold fish include disagreeable person.

cold fish (noun)	unpleasant person (noun)
an aloof unemotional person	a person who is not pleasant or agreeable